It provides basically a subset (maybe around a third) of the same interesting papers that I see in conference proceedings, but it provides them earlier (typically 1 month to 1 year earlier). This can be important as my field (NLP) is quite fast-paced.
Just to give a concrete example, this paper (which was a relevant read for me) was published in TACL in July this year but was available in arXiv since February: https://arxiv.org/abs/1602.01595
I'm in CS (at the intersection of PL/compilers/HPC), and I've never heard of anyone in my field doing that. In fact, the only papers I've read on arxiv have been ones linked on HN.
I'm in a similar intersection (hi!), and same goes for me. I want to change that, though. I have started publishing tech reports (I work in an industry research lab) whenever I submit a paper for review. I'm tired of work being stuck in endless review cycles, not public and not referenceable. Were I still in academia, I would submit to arxiv, and I have even recommended this to grad students.
At least for theoretical CS and cryptography, Crypto ePrint and arXiv often have more detailed full versions of the paper. These are often invaluable for understanding proofs and other important details.
Just to give a concrete example, this paper (which was a relevant read for me) was published in TACL in July this year but was available in arXiv since February: https://arxiv.org/abs/1602.01595